The spatially homogeneous and totally anisotropic Bianchi type-III string cosmological models have been investigated in the presence as well as absence of the magnetic field within the framework of f (R,T) gravity proposed by Harko et al. (Phy. Rev. D: 84, 024020, 2011). The direction of the string has been chosen in z-direction along which the magnetic field is assumed to be present. The string solutions have been discussed in two types: (i) Geometric strings, (ii) String model, where ρ + λ = 0. The energy conditions for a cloud of strings coupled to the Einstein equations have been examined. The physical features of the models have also been discussed.